This general formulation leaves the door open for 2 differing approaches to understanding what the Takana was all about.
- The Sha’ar Hatziyun (242:16) quotes the Eliya Rabba and others who understand that the main objective of the takana was to ensure that the Shabbat clothes were clean when Shabbat arrived. The reason for stressing Thursday was a secondary, precautionary measure to keep the erev-Shabbat schedule open for other things.
- The Sha’ar Hatziyun further quotes the Magen Avraham who disagrees. According to the Magen Avraham, the main intent of Ezra’s takana was to stress that there should be no laundry done on Friday whatsoever. It was not intended to encourage people to clean their Shabbat attire.
According to the Eliya Rabba, since a washing machine provides the clean clothes for Shabbat and still keeps your erev Shabbat schedule wide-open for other preparations, there is no apparent violation of takanat Ezra and this would seemingly be permitted.
According to the Magen Avraham however, Ezra’s takana was no laundry on Friday’s. Period. Apparently no matter how advanced your technology is, there is a Thursday night deadline for cleaning your clothing.
So, like many things in Halacha – I guess it depends who you ask.
P.S.- R’ Nevenzahl (in his comments to the Mishna Berura) writes that today one can be lenient to do laundry with a washing machine erev Shabbat.
R’ Nevenzahl continues by offering an explanation as to why we can forego the takana of Ezra when we usually assume that an official takana cannot be disregarded even if its core rationale is no longer relevant. But according to our understanding of the Eliya Rabba above, I don’t think you need to work so hard for a justification. According to these poskim, the core takana of Ezra was never intended to limit laundry on Friday, but rather to make sure you have clean clothes in a way which won’t overtake your erev Shabbat schedule. Seems like the washing machine is pretty much exactly what Ezra Hasofer had in mind.